If A = begin{bmatrix} 5 & 2 3 & 1 end{bmatri | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) To find the inverse of a $2 	imes 2$ matrix $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$,we use the formula $A^{-1} = \frac{1}{|A|} 	ext{a

Vedclass · Accepted Answer

$\begin{bmatrix} -1 & 2 \ 3 & -5 \end{bmatrix}$

Vedclass · Answer

(B) To find the inverse of a $2 	imes 2$ matrix $A = \begin{bmatrix} a & b \ c & d \end{bmatrix}$,we use the formula $A^{-1} = \frac{1}{|A|} 	ext{adj}(A)$.Given $A = \begin{bmatrix} 5 & 2 \ 3 & 1 \end{bmatrix}$.First,calculate the determinant $|A| = (5)(1) - (2)(3) = 5 - 6 = -1$.Next,find the adjoint matrix $	ext{adj}(A)$ by swapping the diagonal elements and changing the signs of the off-diagonal elements: $	ext{adj}(A) = \begin{bmatrix} 1 & -2 \ -3 & 5 \end{bmatrix}$.Now,$A^{-1} = \frac{1}{-1} \begin{bmatrix} 1 & -2 \ -3 & 5 \end{bmatrix} = \begin{bmatrix} -1 & 2 \ 3 & -5 \end{bmatrix}$.Thus,the correct option is $B$.

If $A = \begin{bmatrix} 5 & 2 \\ 3 & 1 \end{bmatrix}$,then $A^{-1} = $

Similar Questions

If $A = \begin{bmatrix} 4 & 2 \\ 3 & 4 \end{bmatrix}$,then $|adj\,A|$ is equal to

Assertion $(A)$: If $B$ is a $3 \times 3$ matrix and $|B|=6$,then $|\operatorname{Adj}(B)|=36$.
Reason $(R)$: If $B$ is a square matrix of order $n$,then $|\operatorname{Adj}(B)|=|B|^{n}$.

The inverse of the matrix $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$ is

If $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 3 \end{bmatrix}$,then the sum of all elements of $A^{-1}$ is . . . . . . .

If $A, B, C$ are three square matrices such that $AB = AC$ implies $B = C$,then the matrix $A$ is always a/an

Vedclass Test Series

Exam Paper Generator

Online Exam Module